I guess by SSD cable you mean SATA, I'm surprised, if I remember right, those units where IDE. So???
For the white screen it's most likely an unplugged cable. You can also try to use the VGA output, but I'm not sure if you need to enable it in BIOS first...
It is normal that only channel 1 and 4 lights up. It's not because both of them are working or not. It simply in it's initialization process. Same goes for the 1M and 50 ohm LED, both are only for the initialization, don't worry about that, mine does that too! So don't worry!
That thick line is normal, higher bandwidth mean higher noise, so get use to it! It's closer to the reality too (unless it is out of proportion, then it might be the scope).?
The calibrator output is on the same circuit then the AUX out that generates the calibration pattern. So if it doesn't output anything, it might mean the calibrator is defective. If that is the case, you won't be able to do the self cal and you won't be able to fix the two other channels (you might fix them but you need to calibrate them at least one for them to be usable).?
If the ADC were blown, you wouldn't see a line at all or it would be saturated, so that's good. You notice that when you plug something to them, there is a little bounce. depending on what the bounce looks like it might mean several things:
1- if it's just an impulse, it's either caused by coupled capacitance or by the long ground cable
2- if it's continuous and doesn't change if their is a signal or not, it's probably just detecting the probe as an antenna. In that case, you probably have a blown component, hard to say which one.
3- if it's continuous and change depending on signal, it is probably a bad amplifier. It could also be bad calibration factor. With your possibly defective calibrator, I would bet on that. If the calibration factor got corrupted at some point and the calibrator doesn't work, it could very well be simply that. You say you have other Tektronix scope? Use them to verify the output pattern of the AUX out when calibrating a channel and make sure it works properly.?
Considering your 50 ohm impedance is fine, it is unlikely that anything is blown on your signal path. Maybe, you could do this simple test. Plug 2 (1 functional, 1 defective) channels of your scope together to the FGEN. Output a square wave or a triangular wave. Both channel should be on 1M and same configs. Are they match? Then switch the functional channel to 50 ohm and store the waveform. Switch it back to 1M and display the save waveform. Switch the defective channel to 50 ohm. Does the functional channel and the save waveform match? There should be no amplitude or phase mismatch.